Is it possible to have triangles in the line graphs of triangle free graphs? I drew some examples for n=1,2,3,4, and 5 but I don't see any triangles yet.
And what is the explanation behind it if there are or aren't triangles?
Sure -- if the original graph has a vertex of degree 3, then there will be a triangle in the line graph.
The smallest example would be
O / O---O \ O
whose line graph is a triangle.
Or, for a bridgeless example, consider the cube graph.